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`ELECTRIC 1111111
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`HANDBOOK
`
`EDITOR-IN-CHIEF
`L.L.GRIGSBY
`Auburn University
`Auburn, Alabama
`
`CRC PRESS
`
`IEEE PRESS
`
`A CRC Handbook Published in Cooperation with IEEE Press
`
`Titeflex - Exhibit 1031, cover
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`Titeflex - Exhibit 1031, cover
`
`

`

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`Library of Congress Cataloging-in-Publication Data
`
`The electric power engineering handbook / editor-in-chief L.L. Grigsby.
`p. cm. -- (The electrical engineering handbook series)
`Includes bibliographical references and index.
`ISBN 0-8493-8578-4 (alk.)
`1. Electric power production. I. Grigsby, Leonard L. II. Series.
`
`TK1001 .E398 2000
`621.31'2--dc21
`
`00-030425
`
`This book contains information obtained from authentic and highly regarded sources. Reprinted material is
`quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts
`have been made to publish reliable data and information, but the author and the publisher cannot assume
`responsibility for the validity of all materials or for the consequences of their use.
`
`Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or
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`
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`Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
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`
`© 2001 by CRC Press LLC
`
`No claim to original U.S. Government works
`International Standard Book Number 0-8493-8578-4
`Library of Congress Card Number 00-030425
`Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
`Printed on acid-free paper
`
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`Titeflex - Exhibit 1031, page i
`
`Titeflex - Exhibit 1031, page i
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`

`

`4-64
`
`The Electric Power Engineering Handbook
`
`Transmissi
`
`Resistance
`The AC resistance of a conductor in a transmission line is based on the calculation of its DC resistance.
`If DC is flowing along a round cylindrical conductor, the current is uniformly distributed over its cross-
`section area and the DC resistance is evaluated by:
`
`Rd, = —
`P1 [Cl]
`A
`where p = conductor resistivity at a given temperature (S2-m)
`/ = conductor length (m)
`A = conductor cross-section area (m2)
`If AC current is flowing, rather than DC current, the conductor effective resistance is higher due to
`the skin effect (presented in the next section).
`
`(4.15)
`
`Frequency Effect
`The frequency of the AC voltage produces a second effect on the conductor resistance due to the
`nonuniform distribution of the current. This phenomenon is known as skin effect. As frequency increases,
`the current tends to go toward the surface of the conductor and the current density decreases at the
`center. Skin effect reduces the effective cross-section area used by the current and thus the effective
`resistance increases. Also, although in small amount, a further resistance increase occurs when other
`current-carrying conductors are present in the immediate vicinity. A skin correction factor k, obtained
`by differential equations and Bessel functions, is considered to reevaluate the AC resistance. For 60 Hz,
`k is estimated around 1.02:
`
`Rac. = Roc k
`
`(4.16)
`
`Other variations in resistance are caused by:
`
`• temperature
`• spiraling of stranded conductors
`• bundle conductors arrangement
`
`Temperature Effect
`The resistivity of any metal varies linearly over an operating temperature, and therefore the resistance of
`any conductor suffers the same variations. As temperature rises, the resistance increases linearly, according
`to the following equation:
`
`=
`R2
`
`IT F t2 )
`T + t
`
`(4.17)
`
`where R2 = resistance at second temperature t2 (°C)
`R, = resistance at initial temperature t, (°C)
`T = temperature coefficient for the particular material (°C)
`
`Resistivity (p) and temperature coefficient ( T) constants depend on the particular conductor material.
`Table 4.8 lists resistivity and temperature coefficients of some typical conductor materials.
`
`Spiraling and Bundle Conductor Effect
`There are two types of transmission line conductors: overhead and underground. Overhead conductors,
`made of naked metal and suspended on insulators, are preferred over underground conductors because
`of the lower cost and ease of maintenance.
`
`Titeflex - Exhibit 1031, page 4-64
`
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`weight corn
`current. Th(
`of alternate
`surroundin:
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`offers more
`resistance is
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`
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`Titeflex - Exhibit 1031, page 4-64
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`

`

`Handbook
`
`resistance.
`er its cross-
`
`(4.15)
`
`gher due to
`
`due to the
`:y increases,
`eases at the
`he effective
`when other
`k, obtained
`For 60 Hz,
`
`(4.16)
`
`-esistance of
`y, according
`
`(4.17)
`
`:or material.
`
`conductors,
`tors because
`
`Transmission Systerh
`
`4-65
`
`TABLE 4.8 Resistivity and Temperature Coefficient of Some Materials
`
`Material
`
`Resistivity at 20°C (S2-m)
`
`Temperature Coefficient (°C)
`
`Silver
`Annealed copper
`Hard-drawn copper
`Aluminum
`
`1.59 x 10-8
`1.72 x 10-8
`1.77 x 10-8
`2.83 x 10-8
`
`243.0
`234.5
`241.5
`228.1
`
`Aluminum strands
`2 layers,
`30 conductors
`
`Steel strands
`7 conductors
`
`FIGURE 4.51 Stranded aluminum conductor with stranded steel core (ACSR).
`
`In overhead transmission lines, aluminum is a common material because of the lower cost and lighter
`weight compared to copper, although more cross-section area is needed to conduct the same amount of
`current. The aluminum conductor, steel-reinforced (ACSR), is one of the most used conductors. It consists
`of alternate layers of stranded conductors, spiraled in opposite directions to hold the strands together,
`surrounding a core of steel strands as shown in Fig. 4.51. The purpose of introducing a steel core inside
`the stranded aluminum conductors is to obtain a high strength-to-weight ratio. A stranded conductor
`offers more flexibility and is easier to manufacture than a solid large conductor. However, the total
`resistance is increased because the outside strands are larger than the inside strands due to the spiraling.
`The resistance of each wound conductor at any layer, per unit length, is based on its total length as
`follows:
`
`— P
`R
`rend — A
`
`1
`1 + —
`17C
`P
`
`[f2
`
`(4.18)
`
`where R„,,d
`
`= resistance of wound conductor
`
`(Si)
`
`2
`1+I 1E 1
`P
`
`turn
`2rlayer
`
`= length of wound conductor (m)
`
`
`
`wound conductor = relative pitch of
`
`'turn
`2 raver
`= length of one turn of the spiral (m)
`= diameter of the layer (m)
`
`The parallel combination of n conductors with the same diameter per layer gives the resistance per
`layer as follows:
`
`icihni.
`
`L
`
`R y =
`laer
`
`11
`L—d R.
`i=i
`=
`
`(4.19)
`
`Similarly, the total resistance of the stranded conductor is evaluated by the parallel combination of
`resistances per layer.
`
`Titeflex - Exhibit 1031, page 4-65
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`Titeflex - Exhibit 1031, page 4-65
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`